Acar traveled twice as fast on a dry road as it did making the return on a slippery road. the trip was 60 mi each way, and the round trip took 35 hr.

If it was 60 miles round trip, each way was therefore 30 miles.
Let x represent the hours taken on the dry road.  Slippery road was then 2x.  2x + x = 3x.  35 / 3 = 11.66… = x.
So, on the dry road, the car took 11.66…  hours.
For the slippery one, 2 * 11.66… or 23.33…  hours.
Convert to mph, shall we?
Dry road:
30 miles / 11.66… hours = 2.57… mph.
Slippery road:
30 miles / 23.33… hours = 1.28… mph.
If that’s what you’re looking for — you never quite asked.